Răspuns:
(a,b) ∈ {(0,1);(0,3);(1,0);(3,0)}
Explicație pas cu pas:
[tex] \frac{9}{ {a}^{2} + {b}^{2}} \in \mathbb{N} , \ a \in \mathbb{N} , \ b \in \mathbb{N} \\ \implies ({a}^{2} + {b}^{2})\in\{1;3;9\} \\0 \leqslant {a}^{2} \leqslant 9\implies 0 \leqslant a \leqslant 3 \\ 0 \leqslant {b}^{2} \leqslant 9\implies 0 \leqslant b \leqslant 3[/tex]
1)
a = 0 => a² = 0² = 0
b = 1 => b² = 1² = 1
a² + b² = 0 + 1 = 1
2)
a = 0 => a² = 0² = 0
b = 3 => b² = 3² = 9
a² + b² = 0 + 9 = 9
3)
a = 1 => a² = 1² = 1
b = 0 => b² = 0² = 0
a² + b² = 1 + 0 = 1
4)
a = 3 => a² = 3² = 9
b = 0 => b² = 0² = 0
a² + b² = 9 + 0 = 9
=>
(a,b) ∈ {(0,1);(0,3);(1,0);(3,0)}
